Recurrent Marked Temporal Point Processes: Embedding Event History to Vector

Abstract

Large volumes of event data are becoming increasingly avail-able in a wide variety of applications, such as healthcare analytics, smart cities and social network analysis. The precise time interval or the exact distance between two events carries a great deal of information about the dynamics of the underlying systems. These characteristics make such data fundamentally diﬀerent from independently and identically distributed data and time-series data where time and space are treated as indexes rather than random variables. Marked temporal point processes are the mathematical framework for modeling event data with covariates. However, typical point process models often make strong assumptions about the generative processes of the event data, which may or may not reﬂect the reality, and the speciﬁcally ﬁxed para-metric assumptions also have restricted the expressive power of the respective processes. Can we obtain a more expressive model of marked temporal point processes? How can we learn such a model from massive data?

In this paper, we propose the Recurrent Marked Temporal Point Process (RMTPP) to simultaneously model the event timings and the markers. The key idea of our approach is to view the intensity function of a temporal point process as a nonlinear function of the history, and use a recurrent neural network to automatically learn a representation of inﬂuences from the event history. We develop an eﬃcient stochastic gradient algorithm for learning the model parameters which can readily scale up to millions of events. Using both synthetic and real world datasets, we show that, in the case where the true models have parametric speciﬁcations, RMTPP can learn the dynamics of such models with-out the need to know the actual parametric forms; and in the case where the true models are unknown, RMTPP can also learn the dynamics and achieve better predictive performance than other parametric alternatives based on particular prior assumptions.